Archivo por meses: diciembre 2017

Paper “Prime Power Indices in Factorised Groups” published in Mediterr. J. Math.

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M. J. Felipe, A. Martínez Pastor, and V. M. Ortiz-Sotomayor

Prime power indices in factorised groups.

Mediterr. J. Math., 14(6):Art. 225, 15, 2017

https://doi.org/10.1007/s00605-016-0987-9

Abstract

Let the group G=AB be the product of the subgroups A and B. We determine some structural properties of G when the p-elements in A∪B have prime power indices in G, for some prime p. More generally, we also consider the case that all prime power order elements in A∪B have prime power indices in G. In particular, when G=A=B, we obtain as a consequence some known results.

2010 Mathematics Subject Classification: 20D10, 20D40, 20E45, 20D20

Keywords: Finite groups, Products of groups, Conjugacy classes, Sylow subgroups

Paper “Square-free class sizes in products of groups” published in J. Algebra

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M. J. Felipe, A. Martínez Pastor, and V. M. Ortiz-Sotomayor

Square-free class sizes in products of groups

J. Algebra, 491:190–206, 2017

https://doi.org/10.1016/j.jalgebra.2017.08.007

Abstract

We obtain some structural properties of a factorised group G=AB, given that the conjugacy class sizes of certain elements in A∪B are not divisible by p², for some prime p. The case when G=AB is a mutually permutable product is especially considered.

2010 Mathematical Subject Classification: 20D10, 20D40, 20E45

Keywords: Finite groups, Soluble groups, Products of subgroups, Conjugacy classes

 

Paper «K_4-free graphs as a free algebra» published in LIPIcs. Leibniz Int. Proc. Inform., 83

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E. Cosme Llópez, Damien Pous.
K_4-free graphs as a free algebra.
42nd International Symposium on Mathematical Foundations of Computer Science, Art. No. 76, 14 pp., LIPIcs. Leibniz Int. Proc. Inform., 83, Schloss Dagstuhl. Leibniz-Zent. Inform., Wadern, 2017.

doi: 10.4230/LIPIcs.MFCS.2017.76

Abstract:

Graphs of treewidth at most two are the ones excluding the clique with four vertices as a minor. Equivalently, they are the graphs whose biconnected components are series-parallel.
 

We turn those graphs into a free algebra, answering positively a question by Courcelle and Engelfriet, in the case of treewidth two. First we propose a syntax for denoting them: in addition to series and parallel compositions, it suffices to consider the neutral elements of those operations and a unary transpose operation. Then we give a finite equational presentation and we prove it complete: two terms from the syntax are congruent if and only if they denote the same graph.’

2020 Mathematics Subject Classification: 68R10, 68Q45.

Keywords: universal Algebra, graph theory, axiomatisation, graph minors.